The formation of the asteroid belt is believed to be closely linked to the formation of Jupiter, although the exact details are still the subject of ongoing research and study. The leading hypothesis regarding the formation of the asteroid belt around a young Jupiter is known as the "Grand Tack" scenario.
According to this scenario, during the early stages of the solar system, when the gas and dust of the protoplanetary disk were still present, Jupiter started to migrate inward towards the Sun. As Jupiter moved inward, its gravitational influence disturbed the orbits of smaller rocky bodies, preventing them from accreting into larger planets.
As Jupiter migrated, it encountered a region known as the "snow line" where the temperature dropped significantly. In this colder region, the water and other volatile substances in the protoplanetary disk started to condense, forming ice. Jupiter's gravitational pull caused it to capture a large amount of these icy planetesimals, which increased its mass and helped it to halt its inward migration.
Once Jupiter stopped migrating, it started to migrate outward, away from the Sun. During this outward migration, Jupiter's gravitational influence caused a gravitational stirring effect among the smaller rocky bodies, known as planetesimals, in the vicinity. This stirring caused their orbits to become more eccentric and crossed, leading to increased collisions and fragmentation.
The combined effects of Jupiter's inward and outward migration created a region of enhanced collisional activity, resulting in a belt of rocky and icy debris—the asteroid belt—between the orbits of Mars and Jupiter. These fragments are thought to be remnants of the building blocks that were unable to form a planet due to Jupiter's gravitational perturbations.
It's important to note that while the Grand Tack scenario provides a plausible explanation for the formation of the asteroid belt around a young Jupiter, it is still a theoretical model and subject to refinement as new data and observations become available.